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Partially implicit Runge-Kutta methods for wave-like equations in spherical-type coordinates


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      Partially implicit Runge-Kutta methods are presented in this work in order to numerically evolve in time a set of partial differential equations. These methods are designed to overcome numerical instabilities appearing during the evolution of a system of equations due to potential numerical unstable terms in the sources, such as stiff terms or the presence of factors as a result of a particular chosen system of coordinates. In this article, partially implicit Runge-Kutta methods for several convergence orders have been derived and stability properties have been analyzed. These methods are shown to be appropriated to avoid the development of numerical instabilities in the evolution in time of wave-like equations in spherical-type coordinates, in contrast to the explicit Runge-Kutta methods.

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      35L60, 35L05, 83C35
      25 pages, 4 figures
      math-ph gr-qc math.MP


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